Differential Logic • 8

Posted on April 8, 2020 by Jon Awbrey

Propositional Forms on Two Variables

To broaden our experience with simple examples, let’s examine the sixteen functions of concrete type P \times Q \to \mathbb{B} and abstract type \mathbb{B} \times \mathbb{B} \to \mathbb{B}.  Our inquiry into the differential aspects of logical conjunction will pay dividends as we study the actions of \mathrm{E} and \mathrm{D} on this family of forms.

Table A1 arranges the propositional forms on two variables in a convenient order, giving equivalent expressions for each boolean function in several systems of notation.

Table A1.  Propositional Forms on Two Variables

Table A1. Propositional Forms on Two Variables

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Differential Logic • Laws of Form • Peirce (1) (2) (3) (4)

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Differential Logic • 8

  1. Pingback: Survey of Differential Logic • 3 | Inquiry Into Inquiry

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